Taylor expansions of curve-crossing probabilities (Q1962753)
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scientific article; zbMATH DE number 1396204
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Taylor expansions of curve-crossing probabilities |
scientific article; zbMATH DE number 1396204 |
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Taylor expansions of curve-crossing probabilities (English)
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31 January 2000
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A Taylor expansion is obtained for the probability that a Brownian motion hits a smooth nonlinear boundary of the type \(a+\beta t+\varepsilon c(t)\) for small \(\varepsilon> 0\). The proof is based on the Cameron-Martin-Girsanov formula. A probabilistic interpretation of the expansion is given.
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Brownian motion
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Cameron-Martin-Girsanov theorem
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curve-crossing probabilities
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harmonic functions
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